5.1 Answer the following questions regarding earth’s magnetism:

(a) A vector needs three quantities for its specification. Name the three independent quantities conventionally used to specify the earth’s magnetic field.

(b) The angle of dip at a location in southern India is about 18°. Would you expect a greater or smaller dip angle in Britain?

(c) If you made a map of magnetic field lines at Melbourne in Australia, would the lines seem to go into the ground or come out of the ground?

(d) In which direction would a compass free to move in the vertical plane point to, if located right on the geomagnetic north or south pole?

(e) The earth’s field, it is claimed, roughly approximates the field due to a dipole of magnetic moment 8 × 1022 J T^–1 located at its centre. Check the order of magnitude of this number in some way.

(f) Geologists claim that besides the main magnetic N-S poles, there are several local poles on the earth’s surface oriented in different directions. How is such a thing possible at all?

<p><strong>5.1 </strong><strong> (a) </strong>Earth’s magnetic field can be specified by three following independent quantities</p><p>Magnetic declination</p><p>Angle of dip</p><p>Horizontal component of earth’s magnetic field.</p><p><strong> (b)</strong> The angle of dip at a point depends on how far the point is located with respect to North pole or South pole. The angle of dip will be more in Britain than Southern India as Britain is closer to Magnetic North pole than South India to the Magnetic South pole.</p><p><strong> (c)</strong> It is a hypothesis that a huge bar magnet is embedded deep in Earth’s ground with its north pole near magnetic south pole of earth and south pole is near magnetic north pole of earth. Magnetic field lines emanate from a magnetic north pole and terminate at a magnetic south pole. Hence, in a map depicting earth’s magnetic field lines, the field lines at Melbourne, Australia would seem to come out of the ground.</p><p><strong> (d)</strong> If a compass is located on the geomagnetic North pole or South pole, then the compass will be free to move in the horizontal plane while earth’s field is exactly vertical to the magnetic poles. In such case, the compass can point in any direction.</p><p><strong> (e)</strong> Magnetic moment, M = 8 <span contenteditable="false"> <math> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mn>22</mn> </mrow> </mrow> </msup> </math> </span>J<span contenteditable="false"> <math> <msup> <mrow> <mrow> <mi>T</mi> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mrow> </msup> </math> </span></p><p>Radius of the Earth, r = 6.4 <span contenteditable="false"> <math> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mn>6</mn> </mrow> </mrow> </msup> </math> </span>m</p><p>Magnetic field strength is given by the expression:</p><p>B =<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>μ</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> </msub> <mi>M</mi> </mrow> </mrow> <mrow> <mrow> <mn>4</mn> <mi>π</mi> <msup> <mrow> <mrow> <mi>r</mi> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> </msup> </mrow> </mrow> </mfrac> </math> </span> . where <span contenteditable="false"> <math> <msub> <mrow> <mrow> <mi>μ</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> </msub> </math> </span>= Permeability of free space = 4 <span contenteditable="false"> <math> <mi>π</mi> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>7</mn> </mrow> </mrow> </msup> </math> </span>T m<span contenteditable="false"> <math> <msup> <mrow> <mrow> <mi>A</mi> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </mrow> </msup> </math> </span></p><p>Hence, B =<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mn>4</mn> <mi>π</mi> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>7</mn> </mrow> </mrow> </msup> <mo>×</mo> <mn>8</mn> <mi mathvariant="normal"> </mi> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mn>22</mn> </mrow> </mrow> </msup> </mrow> </mrow> <mrow> <mrow> <mn>4</mn> <mi>π</mi> <mo>×</mo> <msup> <mrow> <mrow> <mo> (</mo> <mn>6.4</mn> <mi mathvariant="normal"> </mi> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mn>6</mn> </mrow> </mrow> </msup> <mo>)</mo> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> </msup> </mrow> </mrow> </mfrac> </math> </span> = 0.305 G</p><p><strong> (f)</strong> This quantity is of the order of magnitude of the observed field on earth.Yes, there are several local poles on earth’s surface oriented in different directions. A magnetised mineral deposit is an example of a local N-S pole.</p>

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